A particle $$\(P\)$$ moves in a straight line. It starts at a point $$\(O\)$$ on the line and at time $$\(t\)$$ s after leaving $$\(O\)$$ it has velocity $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$, where $$\(v=4 t^{2}-20 t+21\)$$. Find the distance travelled by $$\(P\)$$ during the time when its velocity is negative. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_43 Year：2020 Question No：5(d)
Answer:
$
s=\int\left(4 t^{2}-20 t+21\right) \mathrm{d} t
$
$
s=\frac{4}{3} t^{3}-10 t^{2}+21 t(+c)
$
$
\frac{49}{6}-\frac{27}{2}
$
Distance \(=\frac{16}{3}=5.33 \mathrm{~m}\)
s=\int\left(4 t^{2}-20 t+21\right) \mathrm{d} t
$
$
s=\frac{4}{3} t^{3}-10 t^{2}+21 t(+c)
$
$
\frac{49}{6}-\frac{27}{2}
$
Distance \(=\frac{16}{3}=5.33 \mathrm{~m}\)
Knowledge points:
4.2.3 use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration Calculus required is restricted to techniques from the content for Paper 1: Pure Mathematics 1.
Solution:
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